Consider a distributional symmetric tensor field \(A\in \mathcal {B}(\Omega ,\operatorname{Sym})\)  such that \(\operatorname{Curl}\operatorname{Curl}A=0\) . In the next lemma we derive the implications of such a curl free tensor field on its restriction to \(\Omega -O\) . We also show that the derived conditions on \(A|_{\Omega -O}\)  are equivalent to \(\operatorname{Curl}\operatorname{Curl}A=0\)  for \(A\)  with negative degree of divergence. These results extend a recent result [1]}, which was meant for tensor fields smooth in \(\Omega -O\) , to tensor fields non-smooth in \(\Omega -O\) .
